Vapilot. (I'll make a small edit to the initial post)
In the case of asymmetric acceleration- from idle to roughly 40%, it's probably less than 2 seconds lag, before acceleration. The acceleration rate being similar between both engines, but with a lag.
For the aircraft with the thrust lever holding at 80%. I'd say both N1 are within 2% upto 80%, The right thrust lever then continues to advance smoothly, while the left is still hesitating.
As for adjustment by maintenance- one engineer has commented that the most reliable function on the aircraft is the autothrottle self test- it's used often, and works every time.